A Dynamic Model for Continuous Lowering Analysis of Deep-Sea Equipment, Based on the Lumped-Mass Method
Abstract
:1. Introduction
2. Mathematical Model and Solution
2.1. Mathematical Model
2.2. Numerical Solution
- (1)
- At t0, the beginning of the solution, Equation (15) is solved with the fourth-order Runge–Cutter method to get the displacement and velocity of each mass point, e.g., and .
- (2)
- At , the whole length of the cable is increased by , and then the element length is increased by . Equation (15) is updated according to Appendix A, and solved to get and . Then the traction in the cable can be calculated through Equations (16) and (17).
- (3)
- Step (2) is repeated until the dedicated lowering depth is achieved.
2.3. Model Validation
3. Results and Discussions
3.1. Lowering Velocity Effect
3.2. Snap Loads
3.3. Damping Effect
3.4. Cable Stiffness Effect
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
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Parameter | Value | |
---|---|---|
Cable | Linear mass, | 24.6 kg/m |
Cross-section area, A | 4098 mm2 | |
Axial stiffness product, EA | 315 MN | |
Equivalent diameter, Dr | 72.23 mm | |
Drag coefficient, | 0.7 | |
Damping ratio, | 0.1 | |
Equipment | Mass, mp | 60 t |
Volume, Vp | 7.63 m3 | |
Vertical projected Area, Ap | 56.95 m2 | |
Added mass, | 300 t | |
Drag coefficient, | 7 |
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Gao, P.; Yan, K.; Ni, M.; Fu, X.; Liu, Z. A Dynamic Model for Continuous Lowering Analysis of Deep-Sea Equipment, Based on the Lumped-Mass Method. Appl. Sci. 2020, 10, 3177. https://doi.org/10.3390/app10093177
Gao P, Yan K, Ni M, Fu X, Liu Z. A Dynamic Model for Continuous Lowering Analysis of Deep-Sea Equipment, Based on the Lumped-Mass Method. Applied Sciences. 2020; 10(9):3177. https://doi.org/10.3390/app10093177
Chicago/Turabian StyleGao, Pan, Keliang Yan, Mingchen Ni, Xuehua Fu, and Zhihui Liu. 2020. "A Dynamic Model for Continuous Lowering Analysis of Deep-Sea Equipment, Based on the Lumped-Mass Method" Applied Sciences 10, no. 9: 3177. https://doi.org/10.3390/app10093177